If you want to block EMI, get an EMI filter, or a socket with integrated filter. Tthat's the easiest way and they're not expensive. Or salvage one from an old PC power-supply, they often come as a separate small board.

Generally, it's 1 X-rated cap between Live and Neutral, 2 Y-rated caps between Live-Ground and Neutral-Ground (sometimes those aren't used, like in the case of double-insulated equipment) and a Common-mode choke.

Something like this is your safest bet, especially because it comes encased in a metal, grounded enclosure:

A simple cap after the trafo won't do you way too much good in that regard.

Ehh? X2 caps are specifically rated for across-the-line duty. You sure as heck can put caps across the mains.

Value depends on frequency and current being filtered. This only matters for SMPS supplies, to prevent conducted noise into the mains. Noise going from line to load is negligible because it's well filtered by design. In your case, the transformer and filter capacitors take out any RFI you could ever worry about.